Refer to the Calculating Sea Ice Concentration from ESMR document for calculations of sea ice concentration from brightness temperatures.

Calculating Sea Ice Concentration from ESMR

Variations in the brightness temperature (T_b) observed over the surface of the Earth are caused by variations in the emissivity of the surface material and variations in physical temperature according to the equation:

T_b = ℇ_T          [1]

This equation is valid for the brightness temperatures of a uniform surface type with emissivit ℇ and physical temperature T. Within the ice pack, the brightness temperatures of a pixel area derives from various sources, including atmospheric contributors as well as the water and ice within the field of view. The brightness temperatures of ice with uniform emissivity is approximated as:

T_b = C_W ℇ_W T_W + C_I ℇ_I T_I + T_A          [2]

Where:

ℇ_W = Emissivity of open water
T_W = Surface physical temperature of open water
C_W = Areal percentage of open water
ℇ_I = Emissivity of sea ice
T_I = Surface physical temperature of sea ice
C_I= Areal percentage of sea ice
T_A= Sum of atmospheric and other above-surface contributions, including direct upwelling radiation from the atmosphere, downwelling radiation reflected by the surface, and radiation from space reflected by the surface. Atmospheric opacity in the polar regions is negligible.

Recognizing that C_W + C_I = 1, the ice concentration C_I, can be determined from Equation [2] as:

C_I = T_b - T₀ / ℇ_I T_eff - T₀          [3]

Where:

T₀ = ℇ_W T_W + T_A, the measured T_b of the water
T_eff = T_I& + T_A / ℇ_I, the effective surface physical temperature.

In the polar regions, the atmospheric contribution to the effective temperature is small because the atmospheric humidity and the water vapor content are very low; therefore, T_eff is equal to T_I. The appropriate value for T_I is the temperature at the top of the sea ice below the snow cover, because most of the observed radiation emanates from a thin top layer of saline ice. In the absence of real-time physical temperature data, T_I is estimated from climatological surface air temperatures in Equation [4] below. The temperature at the top surface of the sea ice is calculated as lying between the surface air temperature T_air -- estimated by mean monthly climatological values -- and the temperature of the water underneath the ice:

T_I = T_air + f(T_f - T_air)          [4]

Where:

T_f = Freezing point of sea water, 271.2 K

f = Empirical parameter determined from the observed brightness temperatures data, by adjusting f until the values of C_I are consistently about 100% during winter. A value of f = 0.25 was used in the Antarctic atlas (Zwally et al. 1983) through examination of the July 1974 data over the Southern Ocean. Later examination of the Northern Hemisphere data showed that f = 0.25 is also appropriate for the Arctic. This value of 0.25 agrees with the overall average of surface measurements made at Pond Inlet in the Canadian Archipelago (R. Ramseier, personal communication). In reality, the magnitude of f varies spatially with the thickness of the ice and snow cover, but f = 0.25 appears to be a reasonable average value.

Analysis of brightness temperatures from the open-ocean area in the vicinity of the ice pack allowed determination of T₀ for use in Equation [1]. Specifically, the four-year average of  brightness temperatures over ice-free areas of the north polar region was calculated from the ESMR observations as 138.3 K. This is the value inserted for T₀. Of the 138.3 K, approximately 120 K derives from the water, and the remainder derives from the atmosphere. In the Antarctic, the similarly calculated T₀ is 135 K. The 3.3 K difference between hemispheres is caused predominantly by actual differences in the average signature of ice-free ocean in the two hemispheres. It could also be caused in part by variations in the sensitivity of the instrument with temperature. The satellite is exposed to solar heating as it approaches the north polar region but not in the south polar region.

The ice concentration parameter is generated from Equation [2] using T₀ = 138.3 K, T_eff = T_I (calculated from Equation [3]), and ℇ_I = 0.92. The emissivity value of 0.92 is estimated from radiative equations appropriate for first-year sea ice, and is confirmed empirically for first-year ice by examination of ESMR data; however, many regions of the Arctic contain significant amounts of multiyear ice, which has an emissivity of approximately 0.84 instead of 0.92; hence, the gridded data can be interpreted directly as ice concentrations only in those grid squares containing open water and first-year sea ice; otherwise, the data should be interpreted using a nomogram in which both ice concentration, C, and multiyear ice fraction, F_MY are represented as variables. The crucial element in the generation of the nomogram is the proper placement of the concentration values on the right-hand scale, corresponding to a field of view with exclusively multiyear ice and open water. The right-hand scale on the nomogram was constructed by recognizing that the concentrations C_I calculated with a first-year ice emissivity were determined by:

C₁ = T_b - T₀ / 0.92T_I - T₀          [5]

Where T₀= 183.3 K.

For multiyear ice, the equation is:

C_MY = T_b - T₀ / 0.84T_I - T₀ = C_I[(0.92T_I- T₀) / (0.84T_I - T₀)]          [6]

Inserting 248 K as an appropriate overall value for T_I, Equation [6] reduces to C_MY = 1.283 C_I, which is the conversion used in creating the nomogram. In the Arctic atlas, the ice concentration maps and nomograms are color-coded, with, for instance, the boundary between light pink and deep brown occurring at 78 percent concentration for first-year ice. During periods of surface melting, first-year and multiyear ice are indistinguishable by passive microwave measurements (Parkinson et al. 1987), and the appropriate scale for both ice types is the scale on the left of the nomogram.

Differences between wet and dry first-year ice, which are about 3 percent, are neglected in the nomogram. The values on tape are termed "pseudo ice concentrations."

This nomogram should be used to interpret pseudo ice concentrations gridded on the magnetic tapes. A given gridded value is associated with a unique ice concentration only if the multiyear ice fraction F_MY is known. For instance, in seasonal sea ice regions with only first-year ice, F_MY = 0. The appropriate scale is shown on the left of the nomogram, so that the gridded values are indeed the calculated ice concentrations. By contrast, in locations where the observed ice field is all multiyear ice (F_MY = 1), then the appropriate scale is on the right-hand side of the nomogram, and the ice concentrations are derived by multiplying the gridded values by 1.283. If no information is known about the multiyear ice fraction, then the nomoram provides the appropriate range of ice concentrations for each gridded value, with the range extending from the gridded value on the left-hand scale to the value horizontally opposite it on the right-hand scale. For instance, a gridded value of 52 percent indicates an ice concentration anywhere from 52 percent (if there is no multiyear ice) to 67 percent (if the ice is all multiyear ice). The nomogram can also be used in an inverted manner to determine the multiyear ice fraction, if there is independent knowledge (or an estimate) of the total ice concentration. This method was done for the Arctic atlas in several cases where the total ice concentration approaches 100 percent.

Processing Steps

GSFC regridded the original ESMR data to a polar stereographic projection. Data gaps in the original data were filled in using a temporal average of the day before and day after, over the entire field. These data do not include ocean masks and weather filters, and days with bad scans still remain. In Autumn 2003, NSIDC reprocessed these data with the following steps:

1. An ocean mask was applied to remove most weather effects and coastal contamination. Refer to the Monthly Ocean Masks and Maximum Extent Masks Web page for more information. The masks are created from SMMR and SSM/I Bootstrap sea ice concentrations. Climatological masks for each month are produced from the length of the time series, November 1978 through September 2002. Any pixel that did not include ice during the time series is classified as ocean. An additional buffer of two pixels (~50 km) is added to the ice edge to make the mask more conservative; thus, the mask is unlikely to mask out legitimate ice retrievals in the ESMR fields. But weather effects in the remaining open water regions, between the ESMR ice edge and the ocean pixels in the mask, are not removed.
    
2. To remove some of the remaining weather effects, fields with a 15 percent threshold of ice concentration are included. Thus, any pixel with less than 15 percent ice is considered ice-free. A value of 200 is added to low ice concentrations (0-15%); thus, values of 200-215 indicate low ice concentration. Low ice concentrations can be recovered by simply subtracting 200 from values greater than or equal to 200. Using 15 percent to define the ice edge is consistent with previous studies showing that the 15 percent isopleth in passive microwave ice concentrations corresponds best with the true ice edge. However, some low ice concentrations may be eliminated with this method. In addition, some weather effects leading to false concentrations greater than 15 percent are not removed.
    
3. Remaining ice concentration errors from bad scans were removed. Errors ranged from a few scan lines to entire fields with bad data, the latter occurring primarily in the Southern Hemisphere. These fields are saved in the bad directory for each hemisphere, on the FTP site. Following is a list of dates for which bad data were removed:
   
   Northern Hemisphere:
   1972: Day 346
   1973: Days 23, 29, 38, 44, 150
   1974: Days 31, 66, 310, 315, 359, 362
   1975: Days 28, 288, 300-302
   1976: Days 40, 98
   1977: Day 131
   
   Southern Hemisphere:
   1973: Days 63-147, 217-241, 266, 280, 284, 287, 297, 334, 335
   1974: Days 13-15, 84-95, 129, 136, 184, 212-220, 252, 295-298, 305
   1975: Days 62, 76, 91-97, 106, 108-115, 117, 150
   1976: Days 217, 272, 314, 334, 346
   1977: Days 72, 88-100 
    
4. Monthly means were created where sufficient data were available, such as a minimum of 10 samples for a given pixel over an entire month. A disadvantage of this approach, however, is that a small number of samples may not represent the true monthly mean ice conditions. To assist users in judging ice conditions, files containing the number of samples at each pixel in the monthly field are included in the monthly directory on the FTP site.
   
   Low ice concentration values in the daily fields were included in the monthly means. After computing the monthly means, ice concentration values below 15 percent were set to 0. The flag values are the same as those for daily grids (see Format above), except without an ocean mask; ocean pixels have a 0 percent concentration. Several months during the ESMR time series did not have sufficient data to create a monthly mean. Table 10 indicates which means were produced for each hemisphere (N and S): 
    

   Table 10. Means Produced for Each Hemispher North

   Months	Years
   	1972	1973	1974	1975	1976	1977
   January		N,S	N,S	N,S	N,S	S
   February		N,S	N,S	N,S	N,S	S
   March			N,S	N,S	N,S	N,S
   April			N,S		N,S
   May			N,S	N,S	N,S
   June		N,S	N,S		N,S
   July		N,S	N,S		N,S
   August			N,S		N,S
   September		N,S	N,S	N,S	N,S
   October		N,S	N,S	N,S	N,S
   November		N,S	N,S	N,S	S
   December	N,S	N,S	N,S	N,S	S

   
   From January 1973 through December 1976, where ESMR provided coverage throughout the year, a climatology was produced for each month by averaging all available years of monthly means for that month. Up to four fields are averaged for each month, one for each year; however, some monthly mean fields were not created due to insufficient data. In these cases, the climatology may be based on more than four years. The flag values in the fields are the same as in the monthly means. These fields are also in the monthly subdirectories within the north and south directories.

The Nimbus-5 flew in a circular sun-synchronous orbit at 1112 km (600 nautical miles), had a local noon (ascending) and midnight (descending) equator crossing, and an 81 degree retrograde inclination. Successive orbits crossed the equator at 27 degree longitude separation. The orbital period was about 107 minutes. Nimbus-5 used an attitude control system which stabilized the spacecraft with respect to the earth and orbital plane, such that the yaw axis pointed normal to the earth and the roll axis aligned with the spacecraft velocity vector, and which also maintained the solar paddles' orientation to the sun. The system permitted fine control of ± 1° in pitch and ± 0.5° in roll and yaw.

These data are derived from Nimbus-5 ESMR brightness temperatures, originally processed by the Goddard Space Flight Center (GSFC). NSIDC obtained the data from GSFC and reproccesed them to remove coastal and weather contamination, and to include a 15 percent ice threshold.